A quick and dirty server. You can set up a webhook to point to it and, whenever the endpoint is hit, it will automatically git pull.

webhook.py

#!/usr/bin/env python3

import http.server
import socketserver
import subprocess

GIT_DIRECTORY='<directory>'
ENDPOINT='/<endpoint>'
PORT=0

class GitHandler(http.server.BaseHTTPRequestHandler):
    def __init__(self, request, client_address, server):
        http.server.BaseHTTPRequestHandler.__init__(self, request, client_address, server)

    def do_POST(self):
        if self.path == ENDPOINT:
            subprocess.Popen(['git', 'pull'], cwd = GIT_DIRECTORY).wait()
            self.send_response(200)
        else:
            self.send_response(404)
        self.end_headers()

if __name__ == '__main__':
    with socketserver.TCPServer(('', PORT), GitHandler) as httpd:
        print('Now running on port', PORT)
        httpd.serve_forever()